Basic Digital Design Discussion D5.4 Section 13.6

Basic Digital Design Sum-of-Products Design Product-of-Sums Design

Sum of Products Design Exclusive-OR Gate XOR X Y Z Z = X ^ Y X Y Z

Sum of Products Design X Y minterms 0 0 m0 = ~X & ~Y 0 1 m1 = ~X & Y 1 0 m2 = X & ~Y 1 1 m3 = X & Y

Sum of Products Design X Y Z Design an XOR gate m1 = ~X & Y m2 = X & ~Y Z = m1 | m2 = (~X & Y) | (X & ~Y)

Sum of Products: Exclusive-OR ~X & Y X & ~Y Z = (~X & Y) | (X & ~Y)

Precedence of Logical Operators All ~ operations are done first All & operations are done next All | operations are done last Z = (~X & Y) | (X & ~Y) = ~X & Y | X & ~Y

Problem

F = ~X & ~Y | X & Y

Basic Digital Design Sum-of-Products Design Product-of-Sums Design

Product of Sums Design Maxterms: A maxterm is NOT a minterm maxterm M0 = NOT minterm m0 M0 = ~m0 = ~(~X & ~Y) = ~~(~~X | ~~Y) = X | Y

Product of Sums Design X Y minterms maxterms 0 0 m0 = ~X & ~Y M0 = ~m0 = X | Y 0 1 m1 = ~X & Y M1 = ~m1 = X | ~Y 1 0 m2 = X & ~Y M2 = ~m2 = ~X | Y 1 1 m3 = X & Y M3 = ~m3 = ~X | ~Y

Product of Sums Design X Y Z Design an XOR gate Z is NOT minterm m0 AND it is NOT minterm m3

Product of Sums Design X Y Z Design an XOR gate M0 = X | Y M3 = ~X | ~Y Z = M0 & M3 = (X | Y) & (~X | ~Y)

Product of Sums: Exclusive-OR